1. 25 Optical Instruments human eye microscopes & telescopes
diffraction & resolution
Homework:
6, 11, 13

2. human eye cornea & lens focus light to retina
flexible lens alters focal length for near & far focus

3. far-sightedness (hyperopia)
cannot focus on near object
correction requires converging lens

4. near-sightedness (myopia)
cannot focus on distant objects
correction requires diverging lens

5. near (NP) and far (FP) points
eye focus: 25cm to very far, i.e. NP = 25cm, FP = infinity
far-sighted: NP > 25cm, corrective lenses allow focus at 25cm, e.g. reading glasses
near-sighted: FP < infinity, corrective lenses allow focus at infinity, e.g. needing glasses to drive a car

6. near-sighted correction
when do = infinity, -di = FP (contacts)
thus -f = FP, 1/f = -1/FP
Ex. looking along ruler, a student cannot focus past 20cm
FP = 20cm
1/f = -1/0.20m = -5.0D

7. far-sighted correction
when do = 25cm, -di = NP (contacts)
thus 1/f = 1/25 - 1/NP (1/do + 1/di)
Ex. a parent reads newspaper at arm’s length, 1.0m
NP = 1.0m
1/f = 1/0.25m - 1/1.0m = +3.0D

8. summary eye/instrument parameters eye defects & corrective lenses
magnifying glass
compound microscope
refracting telescope
diffraction limit of resolution

9. magnifying glass allows close-focus
object at focal point - eye focuses parallel rays which emerge
angular magnification (AM) = 25cm/f
AM = angular-width ratio: with lens vs. when 25cm from eye

10. diffraction & resolution
diffraction thru aperture limits the ability to separate (resolve) two objects
limit of resolution defined = coincidence of 1st dark fringe with CM (below right).
min. angle resolved for single slit = l/w

11. compound microscope maximum AM ~ 2000x
two converging lenses, one close to object (objective), other close to eye (eyepiece), fo < fe
lens/lens distance = “L”

12. optical instruments objective lens faces object
aperture – diameter of light passing through objective lens (can be controlled, e.g. “f-stop”)
small aperture gives large “depth of field”, i.e. near & far are in focus

13. refracting telescope practical maximum AM ~ (2)(apperture(mm))
two converging lenses, fo > fe
lens/lens distance ~ fo + fe